In Washington DC they use small lawn-fences around trees, plants bulbs like Tulips or bedding like Pansies and mulch with Coir. Am sure you can buy decent looking fences like that for £1 or more for better quality ones.

I would level the whole thing or at least terrace it with a large patio area over most of the top. If you really want a dog toilet (not pleasant for anyone) then the bottom terrace would be used for that. It is a lot of work but not an insurmountable one and could be done quite quickly.

Sulphur candles work as you do seem to get less mould. I have tried to burn incense in my GH every few days, just to experiment, and while it is still dampish I see less mould. Wonder if I have stumbled onto something? Not too keen on the smell and it sticks to everything in there.

Why are there no leaves left on it? Did it dry out or get really frosted? If not then give the stem a tug to check the roots. If it is loose or comes away then check for vine weevil grubs. They do re-root well in spring.